1. Field of the Invention
The invention is related generally to resistivity anisotropy interpretation systems and methods for well logging applications. More specifically, the invention is a method of data inversion for determination of formation parameters and for a description of reservoirs.
2. Background of the Art
Electromagnetic induction and wave propagation logging tools are commonly used for determining electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that, when properly interpreted, are diagnostic of the petrophysical properties of the formation and the fluids therein. Normally, wells drilled with non-conductive oil-based mud (OBM) provide an ideal environment for induction logging tools, such as the 3DEXSM. However, in some environments, the drilling industry is turning from the use of OBM to environmentally sensitive water-based mud (WBM) systems. Highly conductive WBM tends to limit the effective dynamic range of formation measurements made with any induction logging tool.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with OBM, Journal of Petroleum Technology, vol. 1, p.148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517 issued to Barber; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al.
U.S. Pat. No. 5,452,761 to Beard et al., the contents of which are fully incorporated herein by reference, discloses an apparatus and method for digitally processing signals received by an induction logging tool comprising a transmitter and a plurality of receivers. An oscillating signal is provided to the transmitter, which causes eddy currents to flow in a surrounding formation. The magnitudes of the eddy currents are proportional to the conductivity of the formation. The eddy currents in turn induce voltages in the receivers. The received voltages are digitized at a sampling rate well above the maximum frequency of interest. The digitizing window is synchronized to a cycle of the oscillating current signal. Corresponding samples obtained in each cycle are cumulatively summed over a large number of such cycles. The summed samples form a stacked signal. Stacked signals generated for corresponding receiver coils are transmitted to a computer for spectral analysis. Transmitting the stacked signals, and not all the individually sampled signals, reduces the amount of data that needs to be stored or transmitted. A Fourier analysis is performed of the stacked signals to derive the amplitudes of in-phase and quadrature components of the receiver voltages at the frequencies of interest. From the component amplitudes, the conductivity of the formation can be accurately derived.
A limitation to the electromagnetic induction resistivity well logging instruments such as that discussed in Beard et al. '761 is that they typically include transmitter coils and receiver coils wound so that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art, these eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, however, are the ones which are typically hydrocarbon-bearing and are of the most interest to the instrument user. Some earth formations which might be of commercial interest therefore may be overlooked by interpreting a well log made using the electromagnetic induction resistivity well logging instruments known in the art.
The effects of formation anisotropy on resistivity logging measurements have long been recognized. Kunz and Moran studied the anisotropic effect on the response of a conventional logging device in a borehole perpendicular to the bedding plane of thick anisotropic bed. Moran and Gianzero extended this work to accommodate an arbitrary orientation of the borehole to the bedding planes.
Rosthal (U.S. Pat. No. 5,329,448) discloses a method for determining the horizontal and vertical conductivities from a propagation or induction well logging device. The method assumes that the angle between the borehole axis and the normal to the bedding plane is known. Conductivity estimates are obtained by two methods. The first method measures the attenuation of the amplitude of the received signal between two receivers and derives a first estimate of conductivity from this attenuation. The second method measures the phase difference between the received signals at two receivers and derives a second estimate of conductivity from this phase shift. Two estimates are used to give the starting estimate of a conductivity model and based on this model. An attenuation and a phase shift for the two receivers are calculated. An iterative scheme is then used to update the initial conductivity model until a good match is obtained between the model output and the actual measured attenuation and phase shift.
U.S. Pat. No. 6,147,496 to Strack et al. teaches the use of an induction logging tool in which at least one transmitter and at least one receiver are oriented in orthogonal directions. By operating the tool at two different frequencies, it is possible to substantially reduce the effect of invasion and to determine the orientation of the tool to the bedding planes Received signals can be written as a series expansion in the frequency, which series expansion contains a term linear in the frequency which is mainly determined by the conductivity in the wellbore region. By combining the equation describing the series expansion of the signals in such a manner that the term linear in the frequency is eliminated, a new set of equations is obtained from which the influence of the wellbore region is virtually eliminated.
U.S. Pat. No. 5,999,883 issued to Gupta et al, (the “Gupta patent”), the contents of which are fully incorporated herein by reference, discloses a method for determination of the horizontal and vertical conductivity of anisotropic earth formations. Electromagnetic induction signals induced by induction transmitters oriented along three mutually orthogonal axes are measured. One of the mutually orthogonal axes is substantially parallel to a logging instrument axis. The electromagnetic induction signals are measured using first receivers each having a magnetic moment parallel to one of the orthogonal axes and using second receivers each having a magnetic moment perpendicular to one of the orthogonal axes which is also perpendicular to the instrument axis. A relative angle of rotation of the perpendicular one of the orthogonal axes is calculated from the receiver signals measured perpendicular to the instrument axis. An intermediate measurement tensor is calculated by rotating magnitudes of the receiver signals through a negative of the angle of rotation. A relative angle of inclination of one of the orthogonal axes which is parallel to the axis of the instrument is calculated, from the rotated magnitudes, with respect to a direction of the vertical conductivity. The rotated magnitudes are rotated through a negative of the angle of inclination. Horizontal conductivity is calculated from the magnitudes of the receiver signals after the second rotation. An anisotropy parameter is calculated from the receiver signal magnitudes after the second rotation. Vertical conductivity is calculated from the horizontal conductivity and the anisotropy parameter.
U.S. Pat. No. 5,889,729 issued to Frenkel et al., the contents of which are fully incorporated herein by reference, discloses a method for acquiring and interpreting wellbore logging data and a method for such interpretation which is significantly faster than previously known methods and which can be used at a well site. Said system produces a final earth model of part of an earth formation having one or more layers. The method includes, in one aspect, generating an initial earth model based on raw data produced by a wellbore logging tool at a location in a borehole through the earth, performing 2-D forward modeling on the initial earth model to produce an interim earth model that includes a set of synthetic tool responses data for the wellbore logging tool, correcting measurements in each layer for shoulder-bed effect, and comparing the synthetic tool response data to the raw data to determine whether there is misfit between them. Various methods of forward modeling can be performed in the case of misfit. The method of Frenkel '729 can be used for any resistivity logging data.
A multi-component device is discussed in U.S. patent application Ser. No. 10/091,310 by Zhang et al, having the same assignee as the present application and the contents of which are incorporated herein by reference. This tool is marketed under the name 3DEXSM by Baker Hughes, Inc. The 3DEXSM device contains three transmitters and three receivers directed along orthogonal axes (x, y, z) with the z-component along the longitudinal axis of the drilling tool. The 3DEXSM tool measures three principal components Hxx, Hyy, Hzz and two cross-components Hxy and Hxz. The 3DEXSM device gives knowledge of resistivities and provides a process for general inversion of data. 3DEXSM is useful in determining orientation, given a sufficient selection of initial conditions. The 3DEXSM device collects data from the non-invaded zone to put in its model. Sensitivity to the initial conditions used in its data inversion affects the 3DEXSM device. There is a need to provide a method of 3DEXSM data interpretation.
Inversion processing of the 3DEX induction data allows the computation of both horizontal (Rh) and vertical (Rv) resistivities, thus allowing the determination of the formation resistivity anisotropy ratio (λ=Rv/Rh). Incorporation of these 3DEX data interpretation results in an enhanced shaly-sand, tensor resistivity petrophysical analysis, leads to reduced evaluation uncertainties and may result in a significant increase in calculated hydrocarbon-in-place reserves over estimates obtained with conventional methodologies. As shown in Frenkel '729, the 2-D inversion problem is subdivided into a sequence of smaller 1-D problems, thereby reducing computing time. For the 2-D inversion process, the vertical magnetic field component, Hzz, of the 3DEX data depends only on the horizontal resistivity, Rh. Therefore, it is possible to perform rapid sequential or even parallel 3DEX data inversion for both Rh and Rv. This can lead immediately to a calculation of resistive anisotropy.
Another technique used in oil exploration is based on galvanic-type well logging measurements. Among these measurements are the Laterolog, Microlaterolog, Array Lateral Log, and other tools.
The Laterolog and Microlaterolog are taught in Doll, H. G., “The Laterolog”, Paper 3198, in Transactions of the AIME, v 192, p. 305-316, 1951, and in Doll, H. G., “The Microlaterolog”, Paper 3492, in Transactions of the AIME, v 198, p. 17-32, respectively. Generally, the Laterolog is an electrode device with multiple current electrodes configured in several different ways to produce several different responses. A current-emitting and current-return electrodes (A and B) are placed close together on the sonde, with a measure electrode (M) several feet away, and a measure return (N) far away. This arrangement is sensitive to the potential gradient between A and B.
The Array Lateral Log technology of data measurements and interpretation is taught in Hakvoort et al. paper “Field Measurements and Inversion Results of the High-Definition Lateral Log”, Paper C, in Transactions of the SPWLA, 1998. It describes a differential array instrument and a method for determining selected parameters of an earth formation surrounding a borehole. This instrument includes a mandrel carrying a single source electrode for injecting an electrical current of a predetermined value into the formation surrounding the borehole, and an array of measurement electrodes uniformly and vertically spaced from the source electrode along the instrument mandrel. The plurality of the Array Lateral Log measurements may be correlated to a plurality of values representative of the selected formation parameters. The plurality of values representative of the selected formation parameters may provide a profile of the selected parameters over an increasing radial distance from the borehole.
In case of highly conductive borehole environments, we cannot neglect the borehole and invaded zone effects in any 3DEX-based data interpretation procedures. There is a need for a method for determination of a stable and unique anisotropy solution in highly conductive borehole environments. The present invention satisfies this need.